Is it possible to play Wii/Gamecube backups on the Wii Black?

I've heard that the DVD drive is incompatible with burned disks on the Wii Black. I was wondering if there was a mod chip that would work, so I can play Gamecube games? I know I could just get an old Wii and have it work, but it wouldn't look nearly as nice next to my old PS3.